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Small perturbations of the Jacobi matrix with weights \sqrt n and zerodiagonal are considered. A formula relating the asymptotics of polynomials ofthe first kind to the spectral density is obtained, which is analogue of theclassical Weyl-Titchmarsh formula for the Schroedinger operator on thehalf-line with summable potential. Additionally a base of generalizedeigenvectors for "free" Hermite operator is studied and asymptotics ofPlancherel-Rotach type are obtained.

Weyl-Titchmarsh type formula for Hermite operator with small perturbation